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We report on the cross-relaxation of Tm 3ϩ in a low phonon energy chloride host. The temperature and concentration dependence for Tm 3ϩ cross-relaxation in the host YCl 3 was studied between 300 and 500 K, in crystals of YCl 3 with concentrations ranging from 0.7 to 7ϫ10 20 ions/cm 3 . Crystals were grown from melts of anhydrous YCl 3 and TmCl 3 powders under Cl 2 atmosphere using a self-seeded vertical Bridgeman technique. Fluorescence spectra and lifetimes resulting from quasi-cw pumping with a 0.5-W, 811-nm diode were collected and analyzed for the spectral region 1100-2000 nm versus temperature for three crystals with varying Tm 3ϩ densities. Each of the fluorescence spectra contain three broad features centered at 1200, 1490, and 1800 nm that reflect the populations of the first three excited levels of Tm 3ϩ . Rates for multiphonon relaxation and cross-relaxation were determined from the fluorescence lifetime data. An increase in 1200-nm fluorescence as the temperature rises is evidence of an endothermic cross-relaxation process. This suggests a fundamentally new mechanism for optical cooling. A macroscopic rate equation model with its temperature and concentration dependence given by theories for phonon-assisted energy transfer is fit to the spectral data.

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We address band engineering in the presence of periodic driving by numerically shaking a lattice containing a bosonic condensate. By not restricting to simplified band structure models we are able to address arbitrary values of the shaking frequency, amplitude, and interaction strengths g. For "near-resonant" shaking frequencies with moderate g, a quantum phase transition to a finite momentum superfluid is obtained with Kibble-Zurek scaling and quantitative agreement with experiment. We use this successful calibration as a platform to support a more general investigation of the interplay between (one particle) Floquet theory and the effects associated with arbitrary g. Band crossings lead to superfluid destabilization, but where this occurs depends on g in a complicated fashion.

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